Solve `sqrt(x-2)+sqrt(4-x)=2.`

Answer

`x = 3`

Explanation

`sqrt(x - 2) + sqrt(4 - x )= 2`
Squaring we get `2 + 4 - x + 2sqrt((x - 2)(4 - x)) = 4`
or ` 2sqrt((x - 4)(2 - x)) = 1`
or `-(x^(2) - 6x + 8 ) = 1`
or `x^(2)- 6x + 9 = 0`
`rArr (x - 3)^(2) = 0 or x = 3`